@ebclr: Unfortunately one rapidly runs out of pins that way.
I've done some documentation of it. Here's a schematic.
Not shown: Arduino Uno
I've also attached a photo as built, and my first cut at a sketch for driving it. Very crude - just multiplexing it in the main loop and counting up in hex from 0000 to FFFF
The display was photographed under normal room lighting with the PWM set for 1/4 brightness. Its showing some flare on the segments, not visible in real life, due to the brightness and the camera's auto aperture & exposure settings.
Photo NotesThe 74HC595 chips U1,2 are top right, with pin 1 to the left.
The ULN2803A chips U3,4 are center right with pin 1 to the right
Q1-12 are on the right top half of the lower board, with Q1 that handled the LSB from U1,U3 on the left. Pinout is B.C.E with E at the rounded end.
+HT is the top bus of the lower breadboad, from AM1S-0524SZ 1W DC-DC converter (bottom right) Pinout is SIL: Vin-, Vin+, Vout-, Vout+. All other busses are +5V at top edge , 0V/Gnd at lower edge of each board.
Decoupling: 2x 0.1uF ceramic disk across U1,U2, 10uF 50V on +HT rail (by DC-DC converter), 47uF 25V, (on right between U2 & U4).
There is some wiring under the VFD so that the four symbols appear in order as the eighth bit of each digit. As VFD anodes and grids are fairly interchangeable from a driver point of view, this is achieved by connecting Grid 3 (centre symbols) to the 'A' anode (which is already under Grid 1), then connecting one of the centre symbol anodes to each remaining grid.
Edit: updated schematic, and zipped code for working clock